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Metamath Proof Explorer

Theorem clmgrp

Description: A subcomplex module is an additive group. (Contributed by Mario Carneiro, 16-Oct-2015)

Ref Expression
Assertion clmgrp ( 𝑊 ∈ ℂMod → 𝑊 ∈ Grp )

Proof

Step Hyp Ref Expression
1 clmlmod ⊢ ( 𝑊 ∈ ℂMod → 𝑊 ∈ LMod )
2 lmodgrp ⊢ ( 𝑊 ∈ LMod → 𝑊 ∈ Grp )
3 1 2 syl ⊢ ( 𝑊 ∈ ℂMod → 𝑊 ∈ Grp )